Inducing Multi-Convexity in Path Constrained Trajectory Optimization for Mobile Manipulators
This provides a more efficient approach for robotics applications involving mobile manipulators, though it appears incremental as it builds on existing optimization techniques.
The paper tackles trajectory optimization for mobile manipulators under multiple constraints by reformulating the non-linear, non-convex problem into a sequence of convex quadratic programs using a multi-affine form and ADMM, enabling parallel computation and solving the cyclicity bottleneck.
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and non-convex problem can be solved as a sequence of convex unconstrained quadratic programs (QPs). This is achieved by reformulating the non-linear constraints that arise out of manipulator kinematics and its coupling with the mobile base in a multi-affine form. We then use techniques from Alternating Direction Method of Multipliers (ADMM) to formulate and solve the trajectory optimization problem. The proposed ADMM has two similar non-convex steps. Importantly, a convex surrogate can be derived for each of them. We show how large parts of our optimization can be solved in parallel providing the possibility of exploiting multi-core CPUs/GPUs. We validate our trajectory optimization on different benchmark examples. Specifically, we highlight how it solves the cyclicity bottleneck and provides a holistic approach where diverse set of trajectories can be obtained by trading-off different aspects of manipulator and mobile base motion.